A330791
Values of k such that A005132(k) (the k-th number in the Recamán sequence) divides k.
Original entry on oeis.org
1, 4, 16, 58, 624, 1520, 8346, 9317, 31221, 240048, 297624, 778144, 2757880, 4670769, 7654224, 24206384, 54806653, 76521364, 260393208, 846807152, 19488644316, 58671741024, 105968380189, 140689013614, 325374626148, 535755688021, 1404720439053, 3116427665348, 3883018238329, 16166305650060
Offset: 1
A005132(4)=2 and 2 divides 4, so 4 is in the sequence.
A330788
Values of k at which the ratio k/A005132(k) sets a new record.
Original entry on oeis.org
1, 4, 31, 62, 64, 111, 129, 131, 30764, 30766, 30768, 56127, 56167, 56199, 56513, 56515, 56827, 99734, 58055311, 904012796, 904032692, 1610175617, 1610178287, 1610186343, 2789149734, 13808214835, 325374625053, 325374625245
Offset: 1
A005132(131) = 4, 131/4 = 32.75, a higher ratio than any smaller term in A005132, so 131 is in the sequence.
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Block[{s = MapIndexed[First[#2]/#1 &, Rest@ Nest[Append[#, If[And[#3 > 0, FreeQ[#1, #3]], #3, #1[[-1]] + #2]] & @@ {#, Length@ #, #[[-1]] - Length@ #} &, {0}, 10^5]], t}, t = Union@ FoldList[Max, Rest@ s]; MapAt[# - 1 &, #, 1] &@ Map[FirstPosition[s, #][[1]] &, t]] (* Michael De Vlieger, Jan 01 2020 *)
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